Isolating and Quantifying the Role of Developmental Noise in Generating Phenotypic Variation

Genotypic variation, environmental variation, and their interaction may produce variation in the developmental process and cause phenotypic differences among individuals. Developmental noise, which arises during development from stochasticity in cellular and molecular processes when genotype and environment are fixed, also contributes to phenotypic variation. While evolutionary biology has long focused on teasing apart the relative contribution of genes and environment to phenotypic variation, our understanding of the role of developmental noise has lagged due to technical difficulties in directly measuring the contribution of developmental noise. The influence of developmental noise is likely underestimated in studies of phenotypic variation due to intrinsic mechanisms within organisms that stabilize phenotypes and decrease variation. Since we are just beginning to appreciate the extent to which phenotypic variation due to stochasticity is potentially adaptive, the contribution of developmental noise to phenotypic variation must be separated and measured to fully understand its role in evolution. Here, we show that variation in the component of the developmental process corresponding to environmental and genetic factors (here treated together as a unit called the LALI-type) versus the contribution of developmental noise, can be distinguished for leopard gecko (Eublepharis macularius) head color patterns using mathematical simulations that model the role of random variation (corresponding to developmental noise) in patterning. Specifically, we modified the parameters of simulations corresponding to variation in the LALI-type to generate the full range of phenotypic variation in color pattern seen on the heads of eight leopard geckos. We observed that over the range of these parameters, variation in color pattern due to LALI-type variation exceeds that due to developmental noise in the studied gecko cohort. However, the effect of developmental noise on patterning is also substantial. Our approach addresses one of the major goals of evolutionary biology: to quantify the role of stochasticity in shaping phenotypic variation

Cooperation of polarized cell intercalations drives convergence and extension of presomitic mesoderm during zebrafish gastrulation

During vertebrate gastrulation, convergence and extension (C&E) movements narrow and lengthen the embryonic tissues, respectively. In zebrafish, regional differences of C&E movements have been observed; however, the underlying cell behaviors are poorly understood. Using time-lapse analyses and computational modeling, we demonstrate that C&E of the medial presomitic mesoderm is achieved by cooperation of planar and radial cell intercalations. Radial intercalations preferentially separate anterior and posterior neighbors to promote extension. In knypek;trilobite noncanonical Wnt mutants, the frequencies of cell intercalations are altered and the anteroposterior bias of radial intercalations is lost. This provides evidence for noncanonical Wnt signaling polarizing cell movements between different mesodermal cell layers. We further show using fluorescent fusion proteins that during dorsal mesoderm C&E, the noncanonical Wnt component Prickle localizes at the anterior cell edge, whereas Dishevelled is enriched posteriorly. Asymmetrical localization of Prickle and Dishevelled to the opposite cell edges in zebrafish gastrula parallels their distribution in fly, and suggests that noncanonical Wnt signaling defines distinct anterior and posterior cell properties to bias cell intercalations

In Silico Characterization of Resonance Energy Transfer for Disk-Shaped Membrane Domains

Förster resonance energy transfer (FRET) has become an important tool to study the submicrometer distribution of proteins and lipids in membranes. Although resolving the two-dimensional distribution of fluorophores from FRET is generally underdetermined, a forward approach can be used to determine characteristic FRET “signatures” for interesting classes of microdomain organizations. As a first step toward this goal, we use a stochastic Monte Carlo approach to characterize FRET in the case of molecules randomly distributed within disk-shaped domains. We find that when donors and acceptors are confined within domains, FRET depends very generally on the density of acceptors within domains. An implication of this result is that two domain populations with the same acceptor density cannot be distinguished by this FRET approach even if the domains have different diameters or different numbers of molecules. In contrast, both the domain diameter and molecule number can be resolved by combining this approach with a segregation approach that measures FRET between donors confined in domains and acceptors localized outside domains. These findings delimit where the inverse problem is tractable for this class of distributions and reframe ways FRET can be used to characterize the structure of microdomains such as lipid rafts

Vaccination strategies to control Ebola epidemics in the context of variable household inaccessibility levels.

Despite a very effective vaccine, active conflict and community distrust during the ongoing DRC Ebola epidemic are undermining control efforts, including a ring vaccination strategy that requires the prompt immunization of close contacts of infected individuals. However, in April 2019, it was reported 20% or more of close contacts cannot be reached or refuse vaccination, and it is predicted that the ring vaccination strategy would not be effective with such a high level of inaccessibility. The vaccination strategy is now incorporating a "third ring" community-level vaccination that targets members of communities even if they are not known contacts of Ebola cases. To assess the impact of vaccination strategies for controlling Ebola epidemics in the context of variable levels of community accessibility, we employed an individual-level stochastic transmission model that incorporates four sources of heterogeneity: a proportion of the population is inaccessible for contact tracing and vaccination due to lack of confidence in interventions or geographic inaccessibility, two levels of population mixing resembling household and community transmission, two types of vaccine doses with different time periods until immunity, and transmission rates that depend on spatial distance. Our results indicate that a ring vaccination strategy alone would not be effective for containing the epidemic in the context of significant delays to vaccinating contacts even for low levels of household inaccessibility and affirm the positive impact of a supplemental community vaccination strategy. Our key results are that as levels of inaccessibility increase, there is a qualitative change in the effectiveness of the vaccination strategy. For higher levels of vaccine access, the probability that the epidemic will end steadily increases over time, even if probabilities are lower than they would be otherwise with full community participation. For levels of vaccine access that are too low, however, the vaccination strategies are not expected to be successful in ending the epidemic even though they help lower incidence levels, which saves lives, and makes the epidemic easier to contain and reduces spread to other communities. This qualitative change occurs for both types of vaccination strategies: ring vaccination is effective for containing an outbreak until the levels of inaccessibility exceeds approximately 10% in the context of significant delays to vaccinating contacts, a combined ring and community vaccination strategy is effective until the levels of inaccessibility exceeds approximately 50%. More broadly, our results underscore the need to enhance community engagement to public health interventions in order to enhance the effectiveness of control interventions to ensure outbreak containment

On Cellular Automaton Approaches to Modeling Biological Cells

We discuss two di#erent types of Cellular Automata (CA): lattice-gasbased cellular automata (LGCA) and the cellular Potts model (CPM), and describe their applications in biological modeling

Interplay between activator-inhibitor coupling and cell-matrix adhesion in a cellular automaton model for chondrogenic patterning

We present a stochastic cellular automaton model for the behavior of limb bud precartilage mesenchymal cells undergoing chondrogenic patterning. This ‘‘agent-oriented’’ model represents cells by points on a lattice that obey rules motivated by experimental findings. The ‘‘cells’’ follow these rules as autonomous agents, interacting with other cells and with the microenvironments cell activities produce. The rules include random cell motion, production and lateral deposition of a substrate adhesion molecule (SAM, corresponding to fibronectin), production and release of a diffusible growth factor (‘‘activator,’’ corresponding to TGF-h) that stimulates production of the SAM, and another diffusible factor (‘‘inhibitor’’) that suppresses the activity of the activator. We implemented the cellular automaton on a two dimensional (2D) square lattice to emulate the quasi-2D micromass culture extensively used to study patterning in avian limb bud precartilage cells. We identified parameters that produce nodular patterns that resemble, in size and distribution, cell condensations in leg-cell cultures, thus establishing a correspondence between in vitro and in silico results. We then studied the in vitro and in silico micromass cultures experimentally. We altered the standard in vitro micromass culture by diluting the initial cell density, transiently exposing it to exogenous activator, suppressing the inhibitor, and constitutively activating fibronectin production. We altered the standard in silico micromass culture in each case by changing the corresponding parameter. In vitro and in silico experiments agreed well. We also used the model to test hypotheses for differences in the in vitro patterns of cells derived from chick embryo forelimb and hindlimb. We discuss the applicability of this model to limb development in vivo and to other organ development

Interplay between activator-inhibitor coupling and cell-matrix adhesion in a cellular automaton model for chondrogenic patterning

We present a stochastic cellular automaton model for the behavior of limb bud precartilage mesenchymal cells undergoing chondrogenic patterning. This ‘‘agent-oriented’’ model represents cells by points on a lattice that obey rules motivated by experimental findings. The ‘‘cells’’ follow these rules as autonomous agents, interacting with other cells and with the microenvironments cell activities produce. The rules include random cell motion, production and lateral deposition of a substrate adhesion molecule (SAM, corresponding to fibronectin), production and release of a diffusible growth factor (‘‘activator,’’ corresponding to TGF-h) that stimulates production of the SAM, and another diffusible factor (‘‘inhibitor’’) that suppresses the activity of the activator. We implemented the cellular automaton on a two dimensional (2D) square lattice to emulate the quasi-2D micromass culture extensively used to study patterning in avian limb bud precartilage cells. We identified parameters that produce nodular patterns that resemble, in size and distribution, cell condensations in leg-cell cultures, thus establishing a correspondence between in vitro and in silico results. We then studied the in vitro and in silico micromass cultures experimentally. We altered the standard in vitro micromass culture by diluting the initial cell density, transiently exposing it to exogenous activator, suppressing the inhibitor, and constitutively activating fibronectin production. We altered the standard in silico micromass culture in each case by changing the corresponding parameter. In vitro and in silico experiments agreed well. We also used the model to test hypotheses for differences in the in vitro patterns of cells derived from chick embryo forelimb and hindlimb. We discuss the applicability of this model to limb development in vivo and to other organ development

On the Use of Ripley's K-Function and Its Derivatives to Analyze Domain Size

Ripley's K-, H-, and L-functions are used increasingly to identify clustering of proteins in membrane microdomains. In this approach, aggregation (or clustering) is identified if the average number of proteins within a distance r of another protein is statistically greater than that expected for a random distribution. However, it is not entirely clear how the function may be used to quantitatively determine the size of domains in which clustering occurs. Here, we evaluate the extent to which the domain radius can be determined by different interpretations of Ripley's K-statistic in a theoretical, idealized context. We also evaluate the measures for noisy experimental data and use Monte Carlo simulations to separate the effects of different types of experimental noise. We find that the radius of maximal aggregation approximates the domain radius, while identifying the domain boundary with the minimum of the derivative of H(r) is highly accurate in idealized conditions. The accuracy of both measures is impacted by the noise present in experimental data; for example, here, the presence of a large fraction of particles distributed as monomers and interdomain interactions. These findings help to delineate the limitations and potential of Ripley's K in real-life scenarios